Fractal Gravity and Bianchi Type-VI Cosmology: Constraints and Observational Viability

In this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy-momentum tensor for a perfect fluid, we solved the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter [Formula: see text] and deceleration parameter [Formula: see text] in terms of cosmic time and redshift also. To determine the model parameters such as [Formula: see text], [Formula: see text], and the hubble constant [Formula: see text], the hubble dataset was analyzed using the [Formula: see text] test. This analysis reveals the best-fit values of [Formula: see text], [Formula: see text][Formula: see text], [Formula: see text], [Formula: see text] and RMSE = 11.4068 matching with the [Formula: see text]CDM model. We carry blow by blow analysis of the model’s characteristics via energy density [Formula: see text], pressure [Formula: see text] and EoS parameter. We examine whether the energy conditions NEC (null energy condition), SEC (strong energy condition), WEC (weak energy condition), and DEC (dominant energy condition) are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the [Formula: see text] CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for [Formula: see text] and [Formula: see text] reveals that [Formula: see text] settles around [Formula: see text] with slight deviation in the range [Formula: see text]. The model closely aligns with [Formula: see text]CDM at higher redshifts. The pair of statefinder diagnostics [Formula: see text] vs. [Formula: see text] is also discussed, and our model for [Formula: see text] represents the [Formula: see text]CDM model.